1. Field of the Invention
The present invention relates to an optical filter formed with a grating having a refractive index change with a predetermined periodicity along an optical axis of an optical waveguide.
2. Related Background Art
Conventionally known is an optical filter formed with a grating having a refractive index change with a predetermined periodicity along an optical axis of an optical waveguide (optical fiber, flat optical waveguide, or the like). Light transmission and reflection characteristics of this optical filter depend on wavelength .lambda. of light, period .LAMBDA. of refractive index change, effective refractive index n.sub.eff, and length L of the area where the grating is formed in its optical axis direction.
In transmission and reflection characteristics of an optical filter formed with a grating having a refractive index changing width with a uniform amplitude, as a general tendency, reflectivity R increases or decreases (transmittance T decreases or increases) respectively depending on whether wavelength is closer to or farther away from Bragg wavelength .lambda..sub.B which satisfies: EQU 2n.sub.eff .multidot..LAMBDA.=m.multidot..lambda..sub.B (1)
where m is a positive integral.
For example, as shown in FIG. 7, in the case of an optical filter in an optical fiber comprising a core 1 and a cladding 3, in which an area of the core 1 is formed with a grating 2 whose refractive index changes along the optical axis with a predetermined pitch .LAMBDA. and a uniform amplitude, when light having a wavelength .lambda. propagated through this optical fiber reaches the optical filter, it is partially transmitted therethrough and the remainder is reflected thereby, depending on the value of wavelength .lambda.. Namely, transmission decreases or increases depending on whether the wavelength is closer to or farther away from Bragg wavelength .lambda..sub.B. FIG. 8 is a graph showing transmission and reflection characteristics of such an optical filter. Here, Bragg wavelength .lambda..sub.B is assumed to be at 1,552.5 nm.
As shown in FIG. 8, reflectivity R is about 1 (i.e., about 0 dB) within a reflection wavelength bandwidth of about 0.3 nm centered at Bragg wavelength .lambda..sub.B, whereas it repeatedly ripples (increases and decreases in the form of mountainous waves) with descending peak levels as the difference between the wavelength .lambda. of the light and Bragg wavelength .lambda..sub.B increases. On the other hand, since this optical filter itself does not absorb light, transmittance T is represented by the following expression: EQU T=1-R (2)
Thus, this optical filter can be used as a band-pass filter which reflects light having a wavelength within a predetermined reflection wavelength band, while transmitting therethrough light outsider the reflection wavelength band.
In the transmission and reflection characteristics of such an optical filter formed with a grating having a uniform amplitude of refractive index changing width, though reflectivity R and transmittance T rise up and fall down acutely near cutoff wavelengths, ripples of reflectivity R having high peak levels also exist in close proximity to the reflection wavelength band. Even when the difference between the wavelength .lambda. and the reflect ion wavelength band increases, the peak level of reflectivity R in each ripple is still high.
An optical filter known as having more excellent transmission and reflection characteristics is the one constituted by a grating whose amplitude of refractive index changing width is defined by a Gaussian function with respect to a positional variable in the optical axis direction (e.g., T. A. Strasser et. al., "UV-induced Fiber Grating OADM Devices for Efficient Bandwidth Utilization," OFC'96, PD8). FIG. 9 is a graph showing an example of transmission and reflection characteristics of thus formed optical filter.
In the case where the amplitude of refractive index changing width is thus defined by a Gaussian function (hereinafter referred to as Gaussian type), as shown in FIG. 9, reflectivity R is about 1 within a reflection wavelength bandwidth of about 0.4 nm centered at Bragg wavelength .lambda..sub.B, whereas it decreases outside the reflection wavelength band. When compared with FIG. 8, it can be seen that, though reflectivity R and transmittance T rise up and fall down near cutoff wavelengths more gradually than in the case with a uniform amplitude of refractive index change (FIG. 8), the peak level of each ripple of reflectivity R outside the reflection wavelength band is lower in the case of Gaussian type (FIG. 9).
Such alteration of transmission and reflection characteristics of an optical filter by making the refractive index change in its grating conform to a certain form of function so as not to become uniform is known as apodization, and thus formed fiber grating is known as apodized fiber grating.
In an optical filter in which the amplitude of refractive index change in the grating is of a Gaussian type as with the above-mentioned conventional example, however, the acuteness in rising and falling of reflectivity R and transmittance T near cutoff wavelengths may not be sufficient.